Economic design of x¯ control charts considering process shift distributions


1 Department of Mechanical Engineering, Andhra University College of Engineering (A), Visakhapatnam, India

2 Department of Mechanical Engineering, Anil Neerukonda Institute of Technology and Sciences, Visakhapatnam, India


Process shift is an important input parameter in
the economic design of control charts. Earlier x control
chart designs considered constant shifts to occur in the
mean of the process for a given assignable cause. This
assumption has been criticized by many researchers since it
may not be realistic to produce a constant shift whenever
an assignable cause occurs. To overcome this difficulty, in
the present work, a distribution for the shift parameter has
been considered instead of a single value for a given
assignable cause. Duncan’s economic design model for x
chart has been extended to incorporate the distribution for
the process shift parameter. It is proposed to minimize total
expected loss-cost to obtain the control chart parameters.
Further, three types of process shifts namely, positively
skewed, uniform and negatively skewed distributions are
considered and the situations where it is appropriate to use
the suggested methodology are recommended.